State of charge preventive control of storage device to stabilize VSI-based microgrid after islanding occurrence using ANN-based control

Abstract

This paper presents an effective method to control the state of charge (SOC) of energy storage system (ESS) installed in a microgrid (MG). Considering voltage and frequency variations after islanding occurrence and based on the stability criteria, MG pre-islanding conditions are divided into secure and insecure classes. It is shown that insecure MG can become secure, if appropriate value for SOC of the ESS is chosen in different conditions of the MG. To select the most important variables of MG, which can estimate proper values of the SOC, a feature selection procedure known as RELIEF is used in this paper. Among all the MG variables, critical ones are selected. Using them, appropriate value of the SOC can be calculated for different conditions of the MG. This approach is economic because it does not change the result of optimal power flow (OPF). In some conditions, the proper control of SOC cannot solely make the MG secure. In these conditions, DGs generated power should be also changed to make the MG secure. This condition leads to a violation from OPF solution and increases the cost of operation. The results demonstrate the effectiveness of the proposed method in comparison with other methods.

Appendix

• (a) Voltage controller The DAEs of voltage controller are as follows [10, 11]:

  $$ \dot{\phi }_{\text{d}} = v_{\text{od,ref}} - v_{\text{od}} $$

  (8)
  $$ \dot{\phi }_{\text{q}} = v_{{{\text{oq}},{\text{ref}}}} - v_{\text{oq}} $$

  (9)
  $$ i_{\text{ld}}^{*} = F \cdot i_{\text{od}} - \omega_{\text{n}} \cdot C_{\text{f}} \cdot v_{\text{oq}} + k_{\text{pv}} \left( {v_{\text{od}}^{*} - v_{\text{od}} } \right)( - v_{\text{od}} ) + k_{\text{iv}} \cdot \phi_{\text{d}} $$

  (10)
  $$ i_{\text{iq}}^{*} = F \cdot i_{\text{oq}} - \omega_{\text{n}} \cdot C_{\text{f}} \cdot v_{\text{od}} + k_{\text{pv}} \left( {v_{\text{oq}}^{*} - v_{\text{oq}} } \right) + k_{\text{iv}} \cdot \phi_{\text{q}} $$

  (11)

  where φ _d and φ _q are the state variable corresponding to voltage PI controller.

• (b) Current controller The DAEs of current controller are as follows [10, 11]:

  $$ \dot{\gamma }_{\text{d}} = i_{\text{id}}^{*} - i_{\text{id}} $$

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  $$ \dot{\gamma }_{\text{q}} = i_{\text{iq}}^{*} - i_{\text{iq}} $$

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  $$ v_{\text{id}}^{*} = - \omega_{\text{n}} \cdot L_{\text{f}} \cdot i_{\text{lq}} + k_{\text{pc}} \left( {i_{\text{lq}}^{*} - i_{\text{lq}} } \right) + k_{\text{ic}} \cdot \gamma_{\text{d}} $$

  (14)
  $$ v_{\text{iq}}^{*} = \omega_{\text{n}} \cdot L_{\text{f}} \cdot i_{\text{ld}} + k_{\text{pc}} \left( {i_{\text{lq}}^{*} - i_{\text{lq}} } \right) + k_{\text{ic}} \cdot \gamma_{\text{q}} $$

  (15)

  where γ _d and γ _q are the state variable corresponding to current PI controller.

• (c) Switching process [10] demonstrates that when the DC voltage is fixed, the switching process can be neglected and the inverter produces the reference voltage (v _i = v _i*). In this condition, the dynamic of primary source has no effect on VSC output voltage. As shown in [10, 11], the fixed DC voltage needs the fast-response energy storage in each VSC.

• (d) Output filter and coupling inductance The DAE of output filter and coupling inductance are as follows [10]:

  $$ \dot{i}_{\text{ld}} = - \frac{{r_{\text{f}} }}{{L_{\text{f}} }}i_{\text{ld}} + \omega_{\text{ref}} i_{\text{lq}} + \frac{1}{{L_{\text{f}} }}v_{\text{id}} - \frac{1}{{L_{\text{f}} }}v_{\text{od}} $$

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  $$ \dot{i}_{\text{lq}} = - \frac{{r_{\text{f}} }}{{L_{\text{f}} }}i_{\text{lq}} - \omega_{\text{ref}} i_{\text{ld}} + \frac{1}{{L_{\text{f}} }}v_{\text{iq}} - \frac{1}{{L_{\text{f}} }}v_{\text{oq}} $$

  (17)
  $$ \dot{v}_{\text{od}} = \omega_{\text{ref}} v_{\text{oq}} + \frac{1}{{C_{\text{f}} }}i_{\text{ld}} - \frac{1}{{C_{\text{f}} }}i_{\text{od}} $$

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  $$ \dot{v}_{\text{oq}} = - \omega_{\text{ref}} v_{\text{od}} + \frac{1}{{C_{\text{f}} }}i_{\text{lq}} - \frac{1}{{C_{\text{f}} }}i_{\text{oq}} $$

  (19)
  $$ \dot{i}_{\text{od}} = - \frac{{r_{\text{c}} }}{{L_{\text{c}} }}i_{\text{od}} + \omega_{\text{ref}} i_{\text{oq}} + \frac{1}{{L_{\text{c}} }}v_{\text{od}} - \frac{1}{{L_{\text{c}} }}v_{\text{bd}} $$

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  $$ \dot{i}_{\text{oq}} = - \frac{{r_{\text{c}} }}{{L_{\text{c}} }}i_{\text{oq}} - \omega_{\text{ref}} i_{\text{od}} + \frac{1}{{L_{\text{c}} }}v_{\text{oq}} - \frac{1}{{L_{\text{c}} }}v_{\text{bq}} $$

  (21)

  where i _ld and i _lq are the direct and quadratic components of filter current, respectively, and other parameters are shown in Fig. 2.

• (e) Load modeling Although many types of load can exist in MGs, a general RL load is considered in this paper. The state equations of the RL load connected at ith node are as follows:

  $$ \frac{{{\text{d}}(i_{{{\text{load}}\,D,i}} )}}{{{\text{d}}t}} = \frac{{ - R_{{{\text{load}}\,i}} }}{{L_{{{\text{load}}\,i}} }}i_{{{\text{load}}\,D,i}} + \omega i_{{{\text{load}}\,Q,i}} + \frac{1}{{L_{{{\text{load}}\,i}} }}v_{bDi} $$

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  $$ \frac{{{\text{d}}(i_{{{\text{load}}\,Q,i}} )}}{{{\text{d}}t}} = \frac{{ - R_{{{\text{load}}\,i}} }}{{L_{{{\text{load}}\,i}} }}i_{{{\text{load}}\,Q,i}} - \omega i_{{{\text{load}}\,D,i}} + \frac{1}{{L_{{{\text{load}}\,i}} }}v_{bQi} $$

  (23)

• (f) Network modeling In a common reference frame, the state equations of line current of i-th line connected between nodes j and k are as follows:

  $$ \frac{{{\text{d}}(i_{{{\text{line}}\,D,i}} )}}{{{\text{d}}t}} = \frac{{ - R_{{{\text{line}}\,i}} }}{{L_{{{\text{line}}\,i}} }}i_{{{\text{line}}\,D,i}} + \omega ii_{{{\text{line}}\,Q,i}} + \frac{1}{{L_{{{\text{line}}\,i}} }}v_{bDi} - \frac{1}{{L_{{{\text{line}}\,i}} }}v_{bDk} $$

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  $$ \frac{{{\text{d}}(i_{{{\text{line}}\,Q,i}} )}}{{{\text{d}}t}} = \frac{{ - R_{{{\text{line}}\,i}} }}{{L_{{{\text{line}}\,i}} }}i_{{{\text{line}}\,Q,i}} - \omega ii_{{{\text{line}}\,D,i}} + \frac{1}{{L_{{{\text{line}}\,i}} }}v_{bQi} - \frac{1}{{L_{{{\text{line}}\,i}} }}v_{bQk} $$

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